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Popular >

expand (x^2-2x-1)^2

Solution

expand

(x^{2} - 2 x - 1)^{2}

Solution

x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1

Solution steps

(x^{2} - 2 x - 1)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x^{2} - 2 x - 1)^{2} = (x^{2} - 2 x - 1) (x^{2} - 2 x - 1)

= (x^{2} - 2 x - 1) (x^{2} - 2 x - 1)

Distribute parentheses

= x^{2} x^{2} + x^{2} (- 2 x) + x^{2} (- 1) - 2 x x^{2} - 2 x (- 2 x) - 2 x (- 1) - 1 \cdot x^{2} - 1 \cdot (- 2 x) - 1 \cdot (- 1)

Simplify

x^{2} x^{2} + x^{2} (- 2 x) + x^{2} (- 1) - 2 x x^{2} - 2 x (- 2 x) - 2 x (- 1) - 1 \cdot x^{2} - 1 \cdot (- 2 x) - 1 \cdot (- 1) : x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1

= x^{4} - 4 x^{3} + 2 x^{2} + 4 x + 1

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Frequently Asked Questions (FAQ)

What is expand (x^2-2x-1)^2 ?
The solution to expand (x^2-2x-1)^2 is x^4-4x^3+2x^2+4x+1